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Motivation plays a key role in student engagement and academic achievement. This study adopts a person-centered approach to examine the longitudinal stability of motivation profiles characterized by self-efficacy, situational interest, and activity achievement emotions. Latent transition analysis identified four motivation profiles across time among physics middle and high school students (N=1,394): High, Moderate, Confident Negative, and Low motivation, with a gradual decline in motivation over two months. Mastery goals predicted membership in higher motivation profiles, whereas performance-approach goals had a minimal association. Students in higher motivation profiles reported greater general, cognitive, behavioral, and emotional engagement, but not greater social engagement. Our findings highlight that organizing classrooms around collaboration rather than competition can improve student motivation and engagement.